Labor is again calling on police to investigate Bronwyn Bishop amid ongoing revelations that the Speaker misused expenses.

Opposition waste watch spokesman Pat Conroy wrote to the Australian Federal Police on Saturday to ask that the agency reconsiders its decision to not investigate whether Ms Bishop committed a serious offence over her use of travel entitlements.

It comes amid fresh claims the embattled Speaker spent $6,000 to hire a luxury corporate aircraft for a 160-kilometre journey from Sydney to Nowra late last year to attend a party fundraiser.

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Labor has renewed calls for the federal police to investigate Speaker Bronwyn Bishop's misused spending on a flight and chopper ride to Liberal fundraisers, as well as travel allowances to her colleagues' weddings

The Speaker made the private flight for a Liberal Party fundraiser on November 22. The 160km trip from Sydney to Berry, south of Nowra, would have taken Ms Bishop just two hours and 21 minutes to drive

The trip came just two weeks after Mrs Bishop's infamous helicopter charter trip from Melbourne to a Liberal fundraiser in Geelong.

Mr Wilkie, who plans to move a no-confidence motion against the Speaker when the parliament resumes, also believes Ms Bishop and her office's 'questionable business dealings' with aircraft charter companies should be investigated by the AFP.

She had been certifying as official travel trips what most people would consider private, he said.

'In my opinion, this is fraud and should be dealt with as a possible criminal matter,' Mr Wilkie said.

Federal Speaker Bronwyn Bishop (circled) has refused to resign over the saga surrounding this $5227 helicopter flight she chartered last year from Melbourne to Geelong. She has spent Thursday morning apologising to taxpayers

Labor will support a no-confidence motion against Ms Bishop, but with the government having the numbers in the House of Representatives, the move is expected to fail.

The government says the Finance Department investigation should be allowed to run its course.

But deputy Liberal leader Julie Bishop admitted the government was having difficulty getting traction on other issues.

'It can be difficult if your surname is Bishop,' Julie Bishop said.

The Speaker's chief of staff, Damien Jones, could not be reached for comment on Saturday.

The Speaker made the $6,000 journey for a Liberal Party fundraiser, for Ann Sudmalis in the marginal seat of Gilmore on November 22.

The 160km trip would have taken the Speaker just two hours and 21 minutes to drive.

Ms Bishop took the flight just a fortnight after her $5,227 chopper ride from Melbourne to Geelong for a separate Liberal fundraiser.

Ms Bishop finally apologised on Thursday for taking the $5,227 helicopter ride after calls for her resignation.

But the Speaker insists she will not resign over the expenses scandal that has engulfed the veteran MP and Abbott government.

Bronwyn Bishop has apologised to taxpayers saying she has 'let them down' over the chartered chopper ride which cost $5227 for her to be transported to a Liberal Party fundraiser last year

Federal Speaker Bronwyn Bishop has finally apologised for her $5000 taxpayer funded chopper ride from Melbourne to Geelong. But she has refused to resign over the saga

Speaker Bronwyn Bishop chartered a helicopter from Melbourne to Geelong at taxpayer expense last year for a Liberal Party event at a golf club

'I want to apologise to the Australian people for my error of judgment and to say sorry,' Mrs Bishop told 2GB early on Thursday morning.

'I feel I've let them down.'

It was an apology the Speaker for the House of Representatives repeated just a few hours later in Sale where she also revealed her regret at not apologising earlier.

Responding to criticism from taxpayers over her flight, which replaced what could have been a one-hour and about 80 kilometre car trip, she admitted: 'They are entitled to do that.'

'The flight was to go to a function in Geelong … all these things, although it's within the rules, it just doesn't look right.'

And she was also challenged on why it had taken three weeks to say sorry.

'I wish I had done it earlier … I love this country very much,' she said.

'I regret that I feel I have let them [Australians] down … I'm going through my expenses now.'

The chartered helicopter is one of many trips taken by the Liberal politician which have been scrutinised including a European trip which came to a whopping $88,000 of taxpayer's money

Mrs Bishop has also pledged to repay all expenses related to her travel to the weddings of Liberal colleagues.

But she insists claiming taxpayer-funded travel allowances to attend the weddings of Sophie Mirabella and Teresa Gambaro was 'technically in the rules'.

She's also asked the prime minister to have all her expenses investigated by the Finance Department.

Ms Bishop said there was no excuse for taking the $5000 helicopter ride.

She has no intention of stepping down from her role as speaker.

'I know that I've disappointed and let down the Australian people, Mrs Bishop added.

'I won't be resigning.'

The Speaker had previously labelled the enquiries into the Melbourne to Geelong helicopter ride as 'a political beat-up' but has now apologised in an radio interview and again at a media conference in Sale

Ms Bishop, who had already admitted she made an 'error of judgment', said she was entitled to make the booking but refunded the money

Independent MP Clive Palmer, who is expected to move a no-confidence motion against the Speaker when parliament resumes in August, accused Mrs Bishop of 'complete bias' in the role.

'She needs to go,' he told the Seven Network.

'We are sick of our politicians with their snout in the trough.'

Labor expects Mrs Bishop to step down before parliament resumes on August 10.

Opposition Leader Bill Shorten said the government would be compromised if it didn't act soon.

'They hope that the whole thing will move on - but it's been lodged in the minds of the Australian people,' he told ABC radio.

Former Labor Speaker Anna Burke says Mrs Bishop should at least stand aside, if not resign.

She accused her successor of bringing parliament into disrepute, saying her position had become untenable.

'It's up to the Speaker herself to actually show some dignity,' Ms Burke told ABC TV.

'You need to do something, otherwise this will drag on.'

Despite the controversy over the chartered helicopter Prime Abbott declared his support for Bronwyn Bishop to remain as Speaker of the House

When the scandal first broke the Federal Speaker described criticism of the $5227 flight as a 'political beat-up'.

Ms Bishop told reporters she was entitled to make the booking but paid back the money because of how expensive the trip was.

'When I saw the figure, it looked large and I thought I should pay it and I'm paying it,' she said.

'Whilst it was in the guidelines, it wasn't satisfactory to have such a large amount of money spent.'

Ms Bishop has also been accused of using taxpayers money to attend a colleague's wedding as she claimed the trip was an 'official business'.

The embattled Speaker claimed $600 for return flights from Sydney to Albury for former Liberal MP Sophie Mirabella's wedding in 2006 and failed to repay the money.

Soon after the coalition was elected in 2003, numerous ministers, including Tony Abbott, were forced to pay back taxpayer expense they claimed to travel to weddings.